(S-AQ 3.59) There are two major tests of readiness for college: the ACT and the

Question

(S-AQ 3.59) There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209. Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. Tanya scores 1362 on the SAT. What is her percentile (± 1)? %

Explanation / Answer

z = (X - Mean)/SD
X = Mean + (z*SD)

z-value corresponding to X = 1362 on the SAT is
z = (1362- 1026)/209 = + 1.60 approximately

X-value corresponding to z = + 1.60 on ACT is
X = 20.9 + (1.6*4.8) = 28.58~26

15) z = (1352 - 1026)/209 = + 1.6
P(Z < z)*100 indicates the percentile
P(Z < 1.66)*100 = 0.9406*100 = 94.06 = 94th Percentile

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